graph

Class Undirected

java.lang.Object

la.la.Value

graph.Graph

graph.Undirected

All Implemented Interfaces:

java.lang.Comparable<Value>

Direct Known Subclasses:

Directed.AsUndirected, Graph.ToUndirected, Undirected.Dense, Undirected.Sparse

public abstract class Undirected
extends Graph

The class of Undirected Graphs. Operations on Undirected Graphs, and special Undirected Graphs. Note that ⟨v0, v1⟩ and ⟨v1, v0⟩ denote the same Edge. Also see Directed and Graph.

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
class	Undirected.AsDirected Treat every Undirected Edge of 'this' Undirected Graph as two Directed Edges (a self-loop remains a single self-loop, now Directed).
static class	Undirected.Dense A Dense, Undirected Graph with Type t and adjacency Matrix A.
class	Undirected.Edge Also see Directed.Edge.
static class	Undirected.K The class of complete Undirected (unlabelled) Graphs, Kn.
static class	Undirected.Sparse The class of Sparse Undirected Graphs.
class	Undirected.Vertex Also see Directed.Vertex.

Nested classes/interfaces inherited from class graph.Graph

Graph.Canonical, Graph.Contraction, Graph.Derived, Graph.Induced, Graph.Renumbered, Graph.SubGraph, Graph.SubGraphs, Graph.ToDirected, Graph.ToUndirected

Nested classes/interfaces inherited from class la.la.Value

Value.Atomic, Value.Bool, Value.Char, Value.Chars, Value.Cts, Value.Defer, Value.Discrete, Value.Enum, Value.Inc_Or, Value.Int, Value.Lambda, Value.List, Value.Maybe, Value.Option, Value.Real, Value.Scannable, Value.Structured, Value.Triv, Value.Tuple

Field Summary

Fields

Modifier and Type	Field and Description
static Type	unlabelled The standard type of Undirected, unlabelled, no self-loops Graphs.
static Type	unlabelled_O Type of Undirected, unlabelled, self-loops (O) allowed Graphs.

Fields inherited from class la.la.Value

C, comparator, CR, E, eight, ffalse, five, fiveR, four, fourR, half, negCR, negOne, negOneR, negTenR, nilVal, nine, None, one, oneR, PI, PIby2, point01, point1, point5, point9, quarter, seven, six, ten, tenR, three, threeR, triv, ttrue, two, twoR, zero, zeroR

Constructor Summary

Constructors

Constructor and Description
Undirected()

Method Summary

Modifier and Type	Method and Description
boolean	adjacent(int v0, int v1) Equivalent to isEdge(v0,v1) for an Undirected Graph (but not for a Directed Graph).
Directed	asDirected() Convenience function.
int	degree(int v) Also see Directed.degree(int).
static Undirected	dense(boolean selfLoops, int[][] A) dense(t,A).
static Undirected	dense(boolean selfLoops, Matrix A) dense(t,A).
static Undirected	dense(int[][] A) dense(false,A) -- no self-loops.
static Undirected	dense(Matrix A) dense(false, A) -- no self-loops.
static Undirected	dense(Type t, int[][] A) dense(t,ints(.,A,.); A must be upper-right triangular.
static Undirected	dense(Type t, Matrix A) Return an Undirected Graph of Type 't' and square symmetric adjacency Matrix 'A'.
static void	main(java.lang.String[] argv) See Test.main(java.lang.String[]).
static Undirected.Sparse	sparse(Type t, int V, int[][] es) Convenience function.
Undirected	toUndirected() Identity function; see Graph.toUndirected().
int[][]	upperRightA() Return the upper-right triangular part of the adjacency (array) Matrix of this Undirected, and hence symmetric, Graph.

Methods inherited from class graph.Graph

A, arrayA, byDegree, byDegree, canonical, canonical1, canonical1R, canonical2, canonical2R, checkProperties, contraction, directPredecessors, directSuccessors, edges, edgesCorrespond, eLabel, eLabelled, eLabels, eSize, eStats, flatten, hashCode, inDegree, induced, isDirected, isEdge, isomorphic, isUndirected, joinedTo, localHash, maxEdges, nAutomorphisms, outDegree, randomised, renumbered, selfLoops, structurallyIdentical, subGraphs, subGraphs, toDirected, type, vLabel, vLabelled, vLabels, vPair2n, vSize

Methods inherited from class la.la.Value

AoM, apply, bOp, compareTo, cons, cts, elt, errMsg, error, force, isTuple, just, n, nElts, nlAoM, pair, print, quad, real, RTE, toString, triple, tuple, UOE, uOp, x

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

unlabelled

public static final Type unlabelled

The standard type of Undirected, unlabelled, no self-loops Graphs.

unlabelled_O

public static final Type unlabelled_O

Type of Undirected, unlabelled, self-loops (O) allowed Graphs.

Constructor Detail

Undirected

public Undirected()

Method Detail

adjacent

public boolean adjacent(int v0,
                        int v1)

Equivalent to isEdge(v0,v1) for an Undirected Graph (but not for a Directed Graph).

Overrides:

adjacent in class Graph

degree

public int degree(int v)

Also see Directed.degree(int). A sub-class may have a more efficient implementation.

Overrides:

degree in class Graph

upperRightA

public int[][] upperRightA()

Return the upper-right triangular part of the adjacency (array) Matrix of this Undirected, and hence symmetric, Graph. If self-loops are prohibited the main (⟨v,v⟩) diagonal is omitted. Also see A(), and Matrix.ints_UR(boolean,int[][],int).

toUndirected

public Undirected toUndirected()

Identity function; see Graph.toUndirected().

Overrides:

toUndirected in class Graph

asDirected

public Directed asDirected()

Convenience function.

dense

public static Undirected dense(Type t,
                               Matrix A)

Return an Undirected Graph of Type 't' and square symmetric adjacency Matrix 'A'. Also see Directed.dense(graph.Type, la.maths.Matrix) and Graph.dense(graph.Type, la.maths.Matrix).

dense

public static Undirected dense(boolean selfLoops,
                               Matrix A)

dense(t,A). 'selfLoops' specifies if Graphs are allowed to have self-loops, not if this Graph actually has any.

dense

public static Undirected dense(Matrix A)

dense(false, A) -- no self-loops.

dense

public static Undirected dense(Type t,
                               int[][] A)

dense(t,ints(.,A,.); A must be upper-right triangular.

dense

public static Undirected dense(boolean selfLoops,
                               int[][] A)

dense(t,A). A must be upper-right triangular.

dense

public static Undirected dense(int[][] A)

dense(false,A) -- no self-loops. A must be upper-right triangular.

sparse

public static Undirected.Sparse sparse(Type t,
                                       int V,
                                       int[][] es)

Convenience function.

main

public static void main(java.lang.String[] argv)

See Test.main(java.lang.String[]).